Subjective Risk Decomposition: A New View for Uncertainty Quantification
Abstract
We present a novel viewpoint for uncertainty quantification. Uncertainty measures are not primitives, in need of axioms and argumentation, but instead consequences, of higher-level modelling decisions. We show how epistemic and aleatoric uncertainty measures can be derived via decomposition of a subjective risk, based on a strictly proper loss. Reverse cross entropy provides a prominent example, where decomposition recovers the classic information-theoretic uncertainty terms. The same approach recovers numerous measures previously proposed across the UQ literature, providing them a common theoretical foundation. This suggests a new approach to UQ: given a modelling scenario and strictly proper loss, the corresponding epistemic and aleatoric terms are induced by the subjective-risk decomposition. We then extend our view to learning theory: we introduce and analyse subjective risk analogues of excess risk, approximation error and estimation error, and identify the connections to UQ. We consider this a first step towards a full learning-theoretic framework for uncertainty quantification.
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BibTeX
@misc{alamri2026subjective,
title = {{Subjective Risk Decomposition: A New View for Uncertainty Quantification}},
author = {Raghad Alamri and Michele Caprio and Gavin Brown},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.15196},
eprint = {2607.15196},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.15196},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Subjective Risk Decomposition: A New View for Uncertainty Quantification
AU - Raghad Alamri
AU - Michele Caprio
AU - Gavin Brown
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2607.15196
UR - https://arxiv.org/abs/2607.15196
AB - We present a novel viewpoint for uncertainty quantification. Uncertainty measures are not primitives, in need of axioms and argumentation, but instead consequences, of higher-level modelling decisions. We show how epistemic and aleatoric uncertainty measures can be derived via decomposition of a subjective risk, based on a strictly proper loss. Reverse cross entropy provides a prominent example, where decomposition recovers the classic information-theoretic uncertainty terms. The same approach recovers numerous measures previously proposed across the UQ literature, providing them a common theoretical foundation. This suggests a new approach to UQ: given a modelling scenario and strictly proper loss, the corresponding epistemic and aleatoric terms are induced by the subjective-risk decomposition. We then extend our view to learning theory: we introduce and analyse subjective risk analogues of excess risk, approximation error and estimation error, and identify the connections to UQ. We consider this a first step towards a full learning-theoretic framework for uncertainty quantification.
ER -